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Shortest Distance of Arbitrary Point from Line Formula

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Shortest Distance of a Point from Line is the perpendicular distance from one arbitrary point to the Line under consideration. Check FAQs

d = mod \underset{̲}{u} s (\frac{(L x \cdot x a) + (L y \cdot y a) + c Line}{\sqrt{({L x}^{2}) + ({L y}^{2})}})

d - Shortest Distance of a Point from Line?L_x - X Coefficient of Line?x_a - X Coordinate of Arbitrary Point?L_y - Y Coefficient of Line?y_a - Y Coordinate of Arbitrary Point?c_Line - Constant Term of Line?

Shortest Distance of Arbitrary Point from Line Example

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Here is how the Shortest Distance of Arbitrary Point from Line equation looks like with Values.

Here is how the Shortest Distance of Arbitrary Point from Line equation looks like with Units.

Here is how the Shortest Distance of Arbitrary Point from Line equation looks like.

9.8387 = mod \underset{̲}{u} s (\frac{(6 \cdot 5) + (-3 \cdot -2) + 30}{\sqrt{(6^{2}) + ({-3}^{2})}})

9.8387 = mod \underset{̲}{u} s (\frac{(6 \cdot 5) + (-3 \cdot -2) + 30}{\sqrt{(6^{2}) + ({-3}^{2})}})

9.8387 = mod \underset{̲}{u} s (\frac{(6 \cdot 5) + (-3 \cdot -2) + 30}{\sqrt{(6^{2}) + ({-3}^{2})}})

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2D Geometry » fx Shortest Distance of Arbitrary Point from Line

Shortest Distance of Arbitrary Point from Line Solution

Follow our step by step solution on how to calculate Shortest Distance of Arbitrary Point from Line?

FIRST Step Consider the formula

d = mod \underset{̲}{u} s (\frac{(L x \cdot x a) + (L y \cdot y a) + c Line}{\sqrt{({L x}^{2}) + ({L y}^{2})}})

Next Step Substitute values of Variables

∴

d = mod \underset{̲}{u} s (\frac{(6 \cdot 5) + (-3 \cdot -2) + 30}{\sqrt{(6^{2}) + ({-3}^{2})}})

Next Step Prepare to Evaluate

∴

d = mod \underset{̲}{u} s (\frac{(6 \cdot 5) + (-3 \cdot -2) + 30}{\sqrt{(6^{2}) + ({-3}^{2})}})

Next Step Evaluate

∴

d = 9.83869910099907

LAST Step Rounding Answer

∴

d = 9.8387

Shortest Distance of Arbitrary Point from Line Formula Elements

Variables

Functions

Shortest Distance of a Point from Line

Shortest Distance of a Point from Line is the perpendicular distance from one arbitrary point to the Line under consideration.

Symbol: d

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Shortest Distance of a Point from Line

Open Variable

X Coefficient of Line

X Coefficient of Line is the numerical coefficient of x in the standard equation of a Line ax+by+c=0 in two dimensional plane.

Symbol: L_x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find X Coefficient of Line

Open Variable

X Coordinate of Arbitrary Point

X Coordinate of Arbitrary Point is the component along the x-axis of an arbitrary point in the two dimensional plane.

Symbol: x_a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find X Coordinate of Arbitrary Point

Open Variable

Y Coefficient of Line

Y Coefficient of Line is the numerical coefficient of y in the standard equation of a Line ax+by+c=0 in two dimensional plane.

Symbol: L_y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Y Coefficient of Line

Open Variable

Y Coordinate of Arbitrary Point

Y Coordinate of Arbitrary Point is the component along the y-axis of an arbitrary point in the two dimensional plane.

Symbol: y_a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Y Coordinate of Arbitrary Point

Open Variable

Constant Term of Line

Constant Term of Line is the numerical value which is not a coefficient of x or y in the standard equation of a Line ax+by+c=0 in two dimensional plane.

Symbol: c_Line

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant Term of Line

Open Variable

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

modulus

Modulus of a number is the remainder when that number is divided by another number.

Syntax: modulus

Other formulas in Line category

Go Shortest Distance of Line from Origin

d Origin = mod \underset{̲}{u} s (\frac{c Line}{\sqrt{({L x}^{2}) + ({L y}^{2})}})

Go X Coefficient of Line given Slope

L x = - (L y \cdot m)

Go Number of Straight Lines using Non Collinear Points

N Lines = C (N Non Collinear, 2)

How to Evaluate Shortest Distance of Arbitrary Point from Line?

Shortest Distance of Arbitrary Point from Line evaluator uses Shortest Distance of a Point from Line = modulus(((X Coefficient of Line*X Coordinate of Arbitrary Point)+(Y Coefficient of Line*Y Coordinate of Arbitrary Point)+Constant Term of Line)/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))) to evaluate the Shortest Distance of a Point from Line, Shortest Distance of Arbitrary Point from Line formula is defined as the perpendicular distance from one arbitrary point to the Line under consideration. Shortest Distance of a Point from Line is denoted by d symbol.

How to evaluate Shortest Distance of Arbitrary Point from Line using this online evaluator? To use this online evaluator for Shortest Distance of Arbitrary Point from Line, enter X Coefficient of Line (L_x), X Coordinate of Arbitrary Point (x_a), Y Coefficient of Line (L_y), Y Coordinate of Arbitrary Point (y_a) & Constant Term of Line (c_Line) and hit the calculate button.

FAQs on Shortest Distance of Arbitrary Point from Line

What is the formula to find Shortest Distance of Arbitrary Point from Line?

The formula of Shortest Distance of Arbitrary Point from Line is expressed as Shortest Distance of a Point from Line = modulus(((X Coefficient of Line*X Coordinate of Arbitrary Point)+(Y Coefficient of Line*Y Coordinate of Arbitrary Point)+Constant Term of Line)/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))). Here is an example- 9.838699 = modulus(((6*5)+((-3)*(-2))+30)/sqrt((6^2)+((-3)^2))).

How to calculate Shortest Distance of Arbitrary Point from Line?

With X Coefficient of Line (L_x), X Coordinate of Arbitrary Point (x_a), Y Coefficient of Line (L_y), Y Coordinate of Arbitrary Point (y_a) & Constant Term of Line (c_Line) we can find Shortest Distance of Arbitrary Point from Line using the formula - Shortest Distance of a Point from Line = modulus(((X Coefficient of Line*X Coordinate of Arbitrary Point)+(Y Coefficient of Line*Y Coordinate of Arbitrary Point)+Constant Term of Line)/sqrt((X Coefficient of Line^2)+(Y Coefficient of Line^2))). This formula also uses Square Root (sqrt), Modulus (modulus) function(s).

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